1. For a rectangular box, the length, ‘l’ is 4centimeters less than thrice the width, ‘w’ in centimeters. Which of the following represents the length of the box in the terms of the width?
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Correct answer is option - 2
Thrice the width means 3w, and since it is 4cm less than thrice the width, it means 3w – 4.
This gives length, l = 3w – 4.
2. Which of the following can be a solution of the equation: |x| = |5x - 2|?
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Correct answer is option - 3
Explanation: Absolute value always splits an equation into two ways: x = 5x - 2 and x = - (5x - 2).
Solving x = 5x – 2 gives x – 5x = -2. This implies -4x = -2 which gives x = 2/4 = 0.5
Similarly, x = -(5x – 2) gives x = -5x + 2. This implies x + 5x = 2 which gives 6x = 2; x = 1/3 = 0.33.
Since 0.33 is not in the options, x = 0.5 is the answer!
3. What is the greatest common factor of the 12, 24 and 30?
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Correct answer is option - 3
Explanation: The prime factorization of 12 = 2 * 2 * 3
The prime factorization of 24 = 2 * 2 * 2 * 3
The prime factorization of 30 = 2 * 3 * 5
GCF is the greatest common factor and the common factor for 12, 24 and 30 is 2 * 3= 6.
4. Two lines intersect each other at a right angle. If the equation of one line is 7x – 2y + 3 = 0, then what is the slope of the second line?
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Correct answer is option - 3
Explanation: The given line can be rearranged as y = (7/2)x + 3/2 which is in the form of y = mx + b.
Therefore the slope of the given line, m_{1} is 7/2.
Two lines intersect each other at right angle implies that they are perpendicular to each other.
The product of slopes of two lines perpendicular to each other is always: m_{1} * m_{2} = -1
Hence slope of the perpendicular line is m_{2} = -2/7.
5. If a + b = √136, ab = 18 and a > b, then what is the value of a – b?
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Correct answer is option - 4
Explanation: (a + b)^{2} = (√136)^{2} gives a^{2} + 2ab + b^{2} = 136 and given ab = 18.
So we get, a^{2} + b^{2} + 36 = 136 implies a^{2} + b^{2} = 136 – 36 = 100.
Therefore we have, (a – b)^{2} = a^{2} – 2ab + b^{2} gives (a – b)^{2} = 100 – (2 * 18) = 100 – 36
So, (a – b)^{2} = 64 which gives a – b = √64 = 8
6. What is the value of x when: 5x – 7 = 7x + 9
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Correct answer is option - 4
Explanation: To solve for x, we should first get all the like terms together on either side of the equation.
Subtracting 7x on both sides, we get 5x – 7x – 7 = 9 which gives -2x – 7 = 9.
Similarly add 7 on both sides to get -2x = 9 + 7 which gives -2x = 16
This gives the answer, x = -8.
7. From the following figure, which of the following gives the value of cos(θ)?
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Correct answer is option - 1
Explanation:
cos(θ) = adjacent side/hypotenuse.
From the given triangle, the adjacent side to the angle ‘θ’ is 9m and the hypotenuse is 15m.
Therefore, cos(θ) = 9/15